Is Chris McDaniel a modern-day Don Quixote tilting at windmills or is he a brave warrior, fighting to the last, for a just cause?

Either way, the tea party candidate’s protracted battle against six-term Sen. Thad Cochran (R) of Mississippi has deepened the split in an already divided Mississippi Republican Party – and is spreading further into the national GOP.

More than three weeks after state Senator McDaniel lost his primary runoff to Senator Cochran by more than 7,600 votes, he is still not conceding the race – and not going away quietly. On Thursday he launches a three-day “Truth and Justice Tour" of Mississippi.

McDaniel claims thousands of improper ballots were cast in the runoff, after an intensive effort by Cochran forces to turn out black, Democratic voters. Democrats were allowed to vote in the GOP runoff as long as they hadn’t voted in the Democratic primary.

McDaniel expects to file a lawsuit in state court by July 26, campaign lawyer Mitch Tyner said Wednesday. Campaign volunteers scouring poll books have found “a lot” of irregularities, including ballot-box stuffing, vote-buying, and illegal “crossover” voting, Mr. Tyner said at a press conference. Tyner said he had enough evidence to sue, but did not present any.

The Cochran campaign has done its own audit of polling books in most counties, and found about 900 “questionable” ballots out of more than 382,000 cast – nowhere close to what would likely be needed to merit tossing out the June 24 result and holding another runoff, which is McDaniel’s goal. The Mississippi Republican Party certified the runoff result on July 7.

"Mississippians are ready to move on," said Cochran adviser Austin Barbour at a press conference Wednesday. Cochran will launch his general election campaign at a county fair on July 31, the campaign announced Thursday.

The prolonged aftermath of the runoff has left Mississippi gasping for air, and has produced schisms within the Republican National Committee and even in another state’s GOP.

Ed Martin, GOP chairman for Missouri and a McDaniel supporter, has called on RNC chairman Reince Priebus to investigate the Mississippi runoff – including what Mr. Martin calls “racially divisive ads and robocalls” against McDaniel. Another top Republican in Missouri called on Martin to stay out of Mississippi’s business.

Within the RNC, Martin appears to have trained his sites on Henry Barbour, a close Priebus ally and the Republican national committeeman for Mississippi who ran a pro-Cochran super political action committee during the primary and runoff.

Henry Barbour, brother of Austin Barbour and nephew of former Mississippi Gov. Haley Barbour (R), funded the outreach to black voters during the runoff, but has denied he did anything improper. In fact, he applauds Cochran’s ability to win over black votes – more than 30,000 in the runoff, by some estimates – as encouraging for GOP party-building. Cochran has a history of good relations with Mississippi’s large black population.

The Mississippi brouhaha is expected to flare up in Chicago in early August, when the Republican National Committee meets to discuss party business.

Conservative activists, including major tea party leaders, are divided on the wisdom of McDaniel’s prolonged fight. Some say privately that they think he doesn’t have a case, and should concede now and live to fight another day. Conservative columnist Ann Coulter said as much publicly last week.

In a meeting with Wall Street Journal editors and reporters this week, Chris Chocola, president of the conservative Club for Growth, also expressed impatience with McDaniel’s prolonged fight.

“If there’s clearly evidence of wrongdoing – that there were ballot integrity issues – I suppose it would be appropriate for him to pursue those, but it would have to be clear,” said Mr. Chocola, whose group invested heavily in supporting McDaniel. “I don’t know that they’re clear at this point.”

Publicly, tea party activists are still all in for McDaniel, who started 2014 as the movement’s best bet to defeat an incumbent GOP senator this cycle. Leaders of major groups released a letter to Priebus Wednesday calling for the RNC to investigate the Mississippi runoff, and “censure” anyone found responsible for improper campaign activities.

All the rabble-rousing appears to have energized the tea party movement.

“Next year, there will be some state races [in Mississippi], and our networks have actually gotten stronger since the end of this election,” says Adam Brandon, communications director for the Washington-based FreedomWorks, which organized volunteers in Mississippi. “We’ve had more sign up to volunteer coming on the heels of the campaign than we had even during the runoff.”

Still, McDaniel’s prolonged battle also may have distracted national tea party efforts in other races. One group says it delayed its focus on GOP primaries in Kansas (Aug. 5) and Tennessee (Aug. 7) as it pressed on in Mississippi.

“We’ve essentially had three weeks of election overtime in Mississippi,” says Kevin Broughton, communications director for the Tea Party Patriots Citizens Fund. “We’re in the process of getting our sea legs back after a pretty all-encompassing race there.”

Conservative groups have also fundraised around Mississippi’s overtime period – as has McDaniel. The Senate Conservatives Fund super political action committee raised $90,000 to support McDaniel’s runoff challenge. During the campaign, the group spent $1.3 million supporting McDaniel.

How McDaniel’s prolonged challenge will affect the November election in Mississippi remains an open question.

For now, emotions are raw and McDaniel supporters insist they would never vote for Cochran. Some may even vote for the Democratic nominee, former Rep. Travis Childers.

“I will NOT vote for Cochran” if he’s still on the ballot in November, says McDaniel supporter Carol Hill from Diamondhead, Miss., in an e-mail. “I may stay home – although that isn't like me and there will be other elections that I will be voting, so I may write in McDaniel's name, knowing it will not be counted. I wouldn't even rule out a vote for the Democrat."

One Mississippi tea partyer says privately that he will definitely vote for Mr. Childers, and has already sent him $199 – one dollar below the amount that would make his donation public.

A survey of Mississippi general election voters released July 15 by the Democratic-leaning firm Public Policy Polling shows Cochran ahead of Childers, 40 percent to 24 percent, and 31 percent undecided. Reform Party candidate Shawn O’Hara got 5 percent.

Cochran came out of the runoff popular with Democrats – 58 percent approval – and unpopular (39 percent) with fellow Republicans. Among African Americans, he has 59 percent approval. Cochran is skilled at steering federal money back home to Mississippi, anathema to the tea party. If he wins reelection, he is likely to become the top Republican on the Appropriations Committee.

Political handicappers say Childers, the Democrat, remains a long shot in November. National Democratic operatives are in watch mode to see if the race is really worth the investment. Democrats are fighting to maintain control of the Senate, and they need to marshal their resources for all the close races they can’t afford to lose.